The volume of the solid is approximately 54.8 cubic cm.
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.
The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
The paraboloid z = 8 - 2x² - 2y² can be written in polar coordinates as z = 8 - 2r². The volume of the solid can be found by using the double integral of the height of the paraboloid over the region defined by the polar coordinates.
In polar coordinates, the region is defined by 0 <= r <= √4 and 0 <= θ <= [tex]\frac{\pi }{2}[/tex]The volume of the solid is given by:
V=[tex]\int\limits \int\limits {(8-2r^{2} )} r\, dr dy[/tex]
= [tex]\int\limits^0_\frac{\pi }{2} {} \, dx\int\limits^0_\sqrt{4} \,}(8-2r^{2})r }dr[/tex]
= [tex]\int\limits^0_\frac{\pi }{2} dx[ {4r^{2} -\frac{2}{3}r^{3} }] \,[/tex] from 0 to sqrt(4)
= [tex]\frac{\pi }{2} [4(4)-(\frac{2}{3}4^{\frac{3}{2} } ][/tex]
= [tex]\frac{\pi }{2}[16-\frac{2}{3}(16^{\frac{1}{2} } )][/tex]
= [tex]\frac{\pi }{2}[16-8({\frac{2^{} \frac{1}{2} }{3} }) ][/tex] cubic cm
So the volume of the solid is approximately 54.8 cubic cm.
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let a and b be two random events. using & as conjunction, ¬ as negation, and the following probabilities:a. P(A & B) = 0.5 b. P(A & ¬ B) = 0.3 c. P(¬ A & B) = 0.1
The value of P(A∪B) is 0.9.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
We are given that
a) P(A∩B) = 0.5
b) P(A ∩ B') = 0.3
c) P(A' ∩ B) = 0.1
When all are added, we get P(A∪B)
So,
P(A∪B) = P(A∩B) + P(A ∩ B')+ P(A' ∩ B) = 0.5 + 0.3 + 0.1 = 0.9
Thus, the value of P(A∪B) is 0.9.
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how many digits are in e2020?
2021 878 877 2020
e2020 has 707 digits.
e is the mathematical constant known as the base of the natural logarithm, which means that the logarithm of any number to the base e is its natural logarithm. It is approximately equal to 2.71828, but its decimal representation goes on infinitely without repeating.
Calculating the number of digits in e2020 involves finding the number of decimal places that e extends past 2020. This is calculated using logarithms.
To find the number of digits in e2020, you can calculate 10^(number of decimal places past 2020) and determine the number of digits in the result.
This gives us 10^(707) = e2020, meaning that e2020 has 707 digits.
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What is the relation between pm to m?
The picometer is a unit of length in the International System of Units (SI), equal to 1×10−12 m, or one trillionth (11000000000000) of a metre, which is the SI base unit of length.
What can a picometer measure?In the International System of Units (SI), the picometer is a unit of length that is equal to 11012 m, or one trillionth (11000000000000) of a metre, the SI base unit of length.
The International Bureau of Weights and Measures uses its international spelling.
In the International System of Units (SI), the picometer is a unit of length that is equal to 11012 m, or one trillionth (11000000000000) of a metre, the SI base unit of length.
The International Bureau of Weights and Measures uses a different international spelling for it, and its SI sign is pm.
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Evaluate the expression using a calculator. Round your answer to two decimal places when appropriate.
Square root 5^32,768 =
The value of the equation is A = ⁵√32,768 is A = 8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ⁵√32,768 be equation (1)
On simplifying the equation , we get
A = 8 x 8 x 8 x 8 x 8 = 32,768
So , the 5th root of ( 32,768 ) is 8
Therefore , the value of A = 8
Hence , the equation is A = 8
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Which oligonucleotide yields reannealing curve A, and which one gives reannealing curve B? Explain your reasoning.
Reannealing curve A is generated by oligonucleotide A, and reannealing curve B is generated by oligonucleotide B. This is because reannealing curves are determined by the sequence, length, and concentration of the oligonucleotides.
Oligonucleotide A and B have different sequences, which will lead to their different reannealing curves. Oligonucleotide A has a higher melting temperature, meaning it will require more energy to reanneal, resulting in a slower reannealing rate.
Oligonucleotide B has a lower melting temperature, meaning it will require less energy to reanneal, resulting in a faster reannealing rate. Therefore, oligonucleotide A will result in reannealing curve A, and oligonucleotide B will result in reannealing curve B.
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a) Name the point(s) in the interior region of the circle.
b) Name the point(s) in the interior region of the triangle
c) Name the line(s) in the interior region of the triangle.
d) Give other name(s) for line p.
a) Note that the points in the interior region of the circle are given as follows;
Point BPoint EPoint G.b) the name of the point(s) in the interior region of the triangle are:
Point Fc) the name of the line(s) in the interior region of the triangle is:
Line [tex]\overline{K}[/tex]d) Another name for the Line [tex]\overline{P}[/tex] is: [tex]\overline{HD}[/tex]
What is a line in geometry?A line is an endlessly long object with no breadth, depth, or curve in geometry.
Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.
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URGENT!! From a point on the ground, a person notices that a 127-foot antenna on the top of a hill subtends an angle of 1.5∘. If the angle of elevation to the bottom of the antenna is 25∘, find the height of the hill.
Answer:
Step-by-step explanation:
To find the height of the hill, we can use the tangent function. Let h be the height of the hill and x be the distance from the person to the base of the hill. We know that:
tan 1.5° = 127 / x
and
tan 25° = h / x
We can use the first equation to find x:
x = 127 / tan 1.5°
And then substitute x into the second equation to find h:
h = x * tan 25° = (127 / tan 1.5°) * tan 25°
This gives us the height of the hill. You can use a calculator to find the value of h.
NEED HELP ASAP - Algebra 2
1. An extraneous solution is a solution that is outside the domain of a function.
2. In a rational function, the solutions must be checked if they belong to the domain, that is, if they do not make the denominator of the function zero.
3. Mikael is wrong as y = -6 is an extraneous solution, as it makes the denominator of y/(y + 6) zero.
What are extraneous solution?An extraneous solution is a solution that is outside the domain of a function, and examples are given as follows:
Negative solution in a problem involving time or any other countable amount.Term that makes the denominator of a rational function zero.A rational function is a function with a variable in the denominator, and the domain of the function is that the denominator cannot assume a value of zero. Hence, each solution must be checked to ensure that it does not make the denominator assume a value of zero.
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Henrietta’s family is on a road trip from New York City to Los Angeles, CA. They have set a goal of reaching the 1,500 mile mark, half way across the country, by the end of the day tomorrow. When they ended their driving today, they had travelled 1,322 miles, and averaged a speed of 60 miles per hour. If they want to meet their goal and travel the same speed, how many whole hours do they need to drive? Solve, check, graph in your looseleaf and below on the canvas as well.
Answer:
Step-by-step explanation:1500-1322=178
178:60=2.9... =>3h
They need to drive for approximately3 hours, to cover the remaining 178 miles and reach their goal of the 1,500-mile mark by the end of the day tomorrow.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
To reach the 1,500-mile mark, Henrietta's family needs to travel an additional 1,500 - 1,322 = 178 miles.
Since they averaged a speed of 60 miles per hour so far, we can use the formula:
distance = speed × time
To find out how long they need to drive to cover the remaining 178 miles. Solving for time, we get,
time = distance/speed
time = 178 miles ÷ 60 miles per hour
time = 2.967 hours
This means they need to drive for approximately3 hours, to cover the remaining 178 miles and reach their goal of the 1,500-mile mark by the end of the day tomorrow.
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6 11 of students at a school are girls. If there are 1309 students at the school, how many are boys?.
There are 595 boys at the school.
A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
The concept is used in this proportion, multiplication and subtraction.
1. First calculate how many students at the school are girls multiplying the total number of students at the school by the proportion of girls:
1309 × [tex]\frac{6}{11}[/tex]
= 714 girls.
2. Then to find out how many students at the school are boys, subtract the number of girls from the total number of students at the school, that is:
1309 - 714
= 595 boys
Therefore, there are 595 boys at the school.
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The total number of boys in school are calculated by ratios in which total of 1309 students are 595 boys.
The number of boys in the school are found by using ratios and proportions. If two ratios are set equal to each other then they are in proportion. Like for an example if there are 2 girls and 5 boys we could write it as the ratio 2:5 (like for every 2 girls, there are 5 boys)
The concept used here is subtraction and multiplication.
i . Given the number of girls in the school are 6/11 of total number of students in the school , so we can find the number of girls by multiplying the proportion of girls with the total number of students.
6/11 * 1309 = 714 girls.
ii . Then to find the total number of boys in the school, we subtract the number of girls from the total number of students. so, by subtracting the number of girls from total number of students we get number of boys as,
1309-714 = 595 boys
Thus , there are total of 595 boys present in the school
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use the big-0 limit lemma to show that log(n) = o(n). then use the limit lemma to show that nx log n = o(nx 1) for any constant x.
The big-O limit lemma states that if f(n) = O(g(n)) as n approaches infinity, then lim n→∞ f(n)/g(n) = C for some constant C.
We must demonstrate that for any constant C > 0, there exists an N such that for all n > N, |log(n)| C*n in order to demonstrate that log(n) = o(n). Here's how to go about it:
For any constant C > 0, choose N = e^C. Then, for all n > N, we have:
log(n) < C
So, |log(n)| < C
And, |log(n)| < C*n
This means that log(n) = o(n), as required.
To show that n^x log(n) = o(n^x) for any constant x, we use the big-O limit lemma. Since log(n) = o(n), we have:
lim n→∞ (n^x log(n))/(n^x) = lim n→∞ log(n)/n^(x-1) = C for some constant C.
Since the limit of the right side is a finite constant, we can conclude that n^x log(n) = o(n^x), as required.
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Hello can anyone explain how to do this question on cosine rules please?
The value of m is obtained as follows:
m = 401º.
How to obtain the cosine function?The cosine function is periodic, meaning that it's behavior is repeated throughout the domain of the function.
For the cosine function, it is positive on the following quadrants.
First quadrant.Fourth quadrant.The point m is the third point that the cosine function passes through the angle of 41º.
Considering that the time time is on the first quadrant of the second lap of the unit circle (each lap is 360º), the value of m is obtained as follows:
m = 360 + 41
m = 401º.
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if you have a population mean and standard deviation of 7 and 3, respectively, what is the z-value when x is 10?
The Z-value represents the number of standard deviations away from the mean a particular value is. To find the Z-value when x is 10, given the population mean and standard deviation of 7 and 3, respectively, we use the following formula:
Z = (X - μ) / σ
Where:
X = 10 (the value of x)
μ = 7 (the population mean)
σ = 3 (the population standard deviation)
Plugging in the values, we get:
Z = (10 - 7) / 3 = 3 / 3 = 1
So the Z-value when x is 10 is 1, which means that x is 1 standard deviation above the mean.
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In each case below list the lettered measures for angles or sides in descending order from greatest to least
On solving the provided question we cans ay that we know that sum of all angles in a triangle is 180 => 55+68 +x = 180 => x = 57
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
in the given triangle,
we have 2 angles given, and
we know that sum of all angles in a triangle is 180
55+68 +x = 180
x = 180 -55-68
x = 57
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Find the quotient. 1/4 divided by 1 /1/2
Answer:
1/6
Step-by-step explanation:
convert the 1 1/2 into a mixed fraction (3/2). Then take the reciprocal of 3/2 (2/3). This becomes 1/4 times 2/3.
1/4 x 2/3 = 2/12
2/12 = 1/6
What is the scale from ABC to DEF? A. 2
B. 1/2
C. 3
Answer:
C: 3
Step-by-step explanation:
Hope this helps!
1. 8 people fit into a 4x4 foot area. Estimate the size of a crowd that is 7 feet deep and 1
mile long on both sides of the street.
Answer:
Below
Step-by-step explanation:
1 mile is 5280 ft
7 x 5280 = 36960 ft^2 for EACH side of the street = 73 920 ft^2 total
4x 4 = 16 ft^2 8ppl / 16 ft^2 = 1 /2 ppl/ft^2
73920 ft^2 * 1/2 ppl / ft^2 = 36 960 people
Prove that the sum of the lengths of the medians of a triangle is greater than half the perimeter.
The proof of the sum of the lengths of the medians of a triangle is greater than half the perimeter is shown below.
What is Triangle Inequality?In Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side;
Given:
We have
In ΔABC
let AB = c , BC = a , CA = b and M is the Median
Now, In ΔCMA using Triangle Inequality
b < m + c/2
and, In ΔCMB using Triangle Inequality
a < m + c/2
Now, adding above two equation we get
a + b < 2m + c (1)
Similarly we can write for other two medians
a+ c < 2n + b (2)
b+ c < 2o+ a (3)
Now, adding (1), (2) and (3) we get
2 (a+b + c)< 2(m + n+ o) + ( a+ +b+ c)
(m+ n + o)> (a+ +b+ c)/ 2
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fundamentals of differential equations and boundary value problems 7th edition
Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.
These equations are used to model a wide range of physical, biological, and chemical processes. The seventh edition of Fundamentals of Differential Equations and Boundary Value Problems by R. Kent Nagle, Edward B. Saff, and Arthur David Snider is a comprehensive textbook that covers the fundamentals of these equations.Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables. It includes topics such as first order equations, higher order linear equations, systems of equations, Laplace transforms, Fourier series, and numerical methods. It also contains a variety of worked examples, exercises, and applications to help students understand the material. Examples include solving initial value problems, boundary value problems, and inverse problems. The book also provides a step-by-step approach to solving problems, including the use of formulas such as the Euler-Cauchy formula, the Picard-Lindelof formula, the Runge-Kutta formula, the Laplace transform, and the Fourier series.
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Complete question:
Find the solution to the differential equation dy/dx + 4y = 0, given the boundary values y(0) = 2 and y(2) = 0.
How to Convert Pint (US) to Milliliter
1 pints = 473.176475 milliliters
Step-by-step explanation:
1pt (US)=473.176479mL
1mL=0.0021133764 pt (US)
for example
covert 15 pt (US) to mL:
15pt (US)= 15 x 473.176473 mL
= 7097.647095 mL
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1 pints is equal to 473.176475 milliliters
How to Convert Pint (US) to Milliliter?
1pt (US)=473.176479mL
1mL=0.0021133764 pt (US)
for example
convert 15 pt (US) to mL:
15pt (US)= 15 x 473.176473 mL
= 7097.647095 mL
The imperial and US customary measurement systems both use the pint as a unit of volume or capacity. Historically, it has been one eighth of a gallon in both of those systems.Because the two systems are defined differently, the British imperial pint is around 20% bigger than the American pint. Although some of them still use the older units known as pints, almost all other nations have standardized on the metric system, therefore the volume varies by regional custom.
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The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $2 per pound to get 200 pounds of the new blend. The selling price of the new blend is to be $2.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
The pounds of the Earl Grey tea and Orange Pekoe tea are required from selling the new blend versus selling the other types is 225 pounds and 75 pounds.
Let x = amount of Earl Grey tea to mix
so, 300-x = amount of Orange Pekoe tea to mix
After putting the equations together,
6x+4(300-x)=5.5*300
6x+1200-4x=1650
2x=450
x=225
So amount of Earl Grey tea to mix is 225 pounds
amount of Orange Pekoe tea to mix = 300-x
300-225 = 75
So the amount of Orange Pekoe tea to mix is 75 pounds.
Amount of Earl Grey tea to mix=225 pounds
Amount of Orange Pekoe tea to mix=75 pounds
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Jaylen brought j cracker and combined them with Marvin’ m cracker. They then plit the cracker equally among 7 friend. A. Type an algebraic expreion that repreent the verbal expreion. Enter your anwer in the box
The algebraic representation of the verbal expression is given by (j + m) / 7.
How to write an algebraic expression?Number of crackers jaylen bought = j
Number of crackers Marvin bought = m
Number of friends shared with = 7
Algebraic expression:
(j + m) / 7
Ultimately, the verbal expression is represented by (j + m) / 7
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What is thee 5th and 23rd term of the pattern 2x+1, 8x-2, and -6.2x+4.5?
Answer:
5th term is 9, 30, and -20.3 and the 23rd term is 45, 174, and -132.9
Step-by-step explanation:
The given pattern consists of three mathematical expressions: 2x + 1, 8x - 2, and -6.2x + 4.5. To find the 5th and 23rd term of the pattern, we need to substitute x with the corresponding value and evaluate the expressions for each of the terms.
For the 5th term:
x = 5-1 = 4
So, the 5th term would be:
2x + 1 = 2 * 4 + 1 = 9
8x - 2 = 8 * 4 - 2 = 30
-6.2x + 4.5 = -6.2 * 4 + 4.5 = -24.8 + 4.5 = -20.3
For the 23rd term:
x = 23-1 = 22
So, the 23rd term would be:
2x + 1 = 2 * 22 + 1 = 45
8x - 2 = 8 * 22 - 2 = 174
-6.2x + 4.5 = -6.2 * 22 + 4.5 = -136.4 + 4.5 = -132.9
Therefore, the 5th term is 9, 30, and -20.3 and the 23rd term is 45, 174, and -132.9 for the given pattern of mathematical expressions.
henry constructed circle A with a radius of 10 units. He then created a sector as shown in the figure below. which of the following expressions would help him find the area
The required expression that represents the area of a sector of circle A is 120/360 × 100π.
What is an area circle?The area of a circle is given by the pie times square of the radius.
Area of circle = πr²
From the quesiton, we have circle A with a radius of 10 units.
The angle of the sector is not defined in the question,
Let the angle of sector Ф = 120°
Formula of area of sector = Ф/360 × πr²,
Assign the value in the above expression,
Area of the sector of circle A = 120 / 360 × π (10)²
Area of th sector of circle A = 120/360 × 100π
Thus, the required expression that represents the area of a sector of circle A is 120/360 × 100π.
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Helena will receive $53 plus $4 per kid for babysitting this afternoon. She is hoping to make at least $68. How many kids does she need to babysit? She writes the inequality 4x+53≥68, where x equals the number of kids, to help figure this out. Solve her inequality. Use the letter x as your variable and write your x term first.
Helena would need to babysit at least 4 kids.
What are Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Helena will receive $53 plus $4 per kid for babysitting this afternoon.
Let x be the number of kids that she babysit.
Given the inequality can be written as,
4x + 53 ≥ 68
4x ≥ 68 - 53
4x ≥ 15
x ≥ 3.75 ≈ 4
Hence Helena should babysit 4 kids in order to get at least $68.
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let r be the region bounded by the curve y=x−−√ and the lines x=0 and y=6.
The area of r is 18.
1. First, we need to find the intersection of the curve and the line y = 6. We can do this by setting the two equations equal to each other and solving for x.
y = x−−√
y = 6
x = 6
2. Next, we need to calculate the area of the region. We can do this by using the formula for the area of a triangle.
A = 1/2 * base * height
A = 1/2 * 6 * (6 - √6)
A = 18
Therefore, the area of the region r is 18.
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We have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this?A)6 B)10 C)30 D)60
We can create a committee with 2 women and 2 men in (D) 60 ways.
To find the number of ways to select 2 women out of 4, we can use the combination formula C(4, 2) = 4! / (2! * (4 - 2)!) = 6. Similarly, to select 2 men out of 5, we can use the combination formula C(5, 2) = 5! / (2! * (5 - 2)!) = 10. To find the total number of ways to create a committee with 2 women and 2 men, we need to multiply the number of ways to select women and men: 6 * 10 = 60.
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Bold u times left parenthesis Bold v plus Bold w right parenthesis equals Bold u times Bold v plus Bold u times Bold wu×(v+w)=u×v+u×w
always true or not always true? Explain the answer.
A. This is always true by the distributive property.
B. This is always true because it is a property of a cross product.
C. This is not true when vectors v and w are parallel.
D. This is not always true because when the vectors v and w go in opposite directions this is not true.
Bold u times left parenthesis Bold v plus Bold w right parenthesis equals Bold u times Bold v plus Bold u times Bold wu×(v+w)=u×v+u×w
always true or not always true? Explain the answer.
A. This is always true by the distributive property.
B. This is always true because it is a property of a cross product.
C. This is not true when vectors v and w are parallel.
D. This is not always true because when the vectors v and w go in opposite directions this is not true.
The equation u×(v + w) = (u × v) + (u × w) is generally true as a property of the cross product.
The cross product is a mathematical operation that results in a third vector that is perpendicular to both input vectors.
The equation u×(v + w) = (u × v) + (u × w) is a mathematical expression that relates the cross product of two vectors, v and w, to the cross product of each vector individually with a third vector, u.
In general, the equation is true, as it is a property of the cross product which is property is known as the distributive property.
However, there are certain conditions where the equation is not always true.
Therefore, the correct option is (b).
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(c) what is the probability that the two sample proportions will differ by more than 0. 05 ?.
Answer:
0.05
Step-by-step explanation:
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0.05
Find the equation in slope- intercept form that matches the table of solutions.
The final equation in slope-intercept form is y = x - 3.
What do you mean by slope?The slope of a line is a number that describes the steepness of the line and the direction in which the line is increasing or decreasing. It is defined as the ratio of the change in the vertical distance (y) to the change in the horizontal distance (x) between two points on the line. The slope can be calculated as the rise over run and is often represented by the letter "m". Slope is an important concept in mathematics, particularly in algebra and geometry, as it provides information about the direction and the rate of change of a line.
The equation in slope-intercept form can be found using the pattern in the table. The slope of the line can be found by finding the difference in y-values and dividing by the difference in x-values between two points on the line. In this case, the slope is equal to 1, so the equation can be written as y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, use one of the points from the table and plug in the x and y values into the equation. Using the point (0, -3), we get -3 = 1 * 0 + b, so b = -3. The final equation in slope-intercept form is y = x - 3.
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